Hide stark indignation, though they're gutted (4)
I believe the answer is:
skin
'hide' is the definition.
(a hide is an animal skin)
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for skin that I've seen before include "What keeps you in" , "Hide - flay" , "External surface" , "Outer surface" , "Living tissue" .)